Certainly! Let's simplify the expression [tex]\(\left(y^{-2}\right)^2\)[/tex] step-by-step and express the answer without using negative exponents.
1. Start with the given expression:
[tex]\[
\left(y^{-2}\right)^2
\][/tex]
2. Apply the power of a power property [tex]\( (a^m)^n = a^{m \cdot n} \)[/tex] to the expression:
[tex]\[
\left(y^{-2}\right)^2 = y^{-2 \cdot 2} = y^{-4}
\][/tex]
3. Convert the negative exponent to a positive exponent using the property [tex]\( a^{-m} = \frac{1}{a^m} \)[/tex]:
[tex]\[
y^{-4} = \frac{1}{y^4}
\][/tex]
Therefore, the simplified expression without negative exponents is:
[tex]\[
\frac{1}{y^4}
\][/tex]
This is the final result.
